Problem: Simplify the following expression: $k = \dfrac{50s^2 + 50ts}{20s^2 + 60rs} - \dfrac{20ts + 60s^2}{20s^2 + 60rs}$ You can assume $r,s,t \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{50s^2 + 50ts - (20ts + 60s^2)}{20s^2 + 60rs}$ $k = \dfrac{-10s^2 + 30ts}{20s^2 + 60rs}$ The numerator and denominator have a common factor of $10s$, so we can simplify $k = \dfrac{-s + 3t}{2s + 6r}$